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Integral of x*dx/(x+1) dx
The solution
Detail solution
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Rewrite the integrand:
x1⋅x+11=1−x+11
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Integrate term-by-term:
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The integral of a constant is the constant times the variable of integration:
∫1dx=x
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The integral of a constant times a function is the constant times the integral of the function:
∫(−x+11)dx=−∫x+11dx
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Let u=x+1.
Then let du=dx and substitute du:
∫u1du
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The integral of u1 is log(u).
Now substitute u back in:
log(x+1)
So, the result is: −log(x+1)
The result is: x−log(x+1)
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Add the constant of integration:
x−log(x+1)+constant
The answer is:
x−log(x+1)+constant
The answer (Indefinite)
[src]
/
|
| 1
| x*1*----- dx = C + x - log(1 + x)
| x + 1
|
/
x−log(x+1)
The graph
=
1−log(2)
Use the examples entering the upper and lower limits of integration.